求y=x^n⼀(1-x)的n阶导数

2025-06-27 02:14:25
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回答1:

改写  y = (x^n)/(1-x)  = {[(x^n)-1]+1}/(1-x) = {[x^(n-1)] + [x^(n-2)] + … + x + 1} + 1/(1-x),因此,  y' = {(n-1)[x^(n-2)] + (n-2)[x^(n-3)] + … + 1} + 1/(1-x)^2,  y" = {(n-1)(n-2)[x^(n-3)] + ...